 # Factors of 70

The factors of 70 are the numbers, that produce the result as 70 when two numbers are multiplied together. Consider an example, the factor pairs of 67 is written as (1, 67) and (-1,-67). When we multiply the pair of negative factors, the result should give the original number, such as multiplying -1 × -67, then we get the number 67. Thus, we can consider both positive and negative factor pairs of 67. Factor pairs of the number 70 are the whole numbers which could be either positive or negative but not a fraction or decimal number. To find the factors of a number, 70, we will use the factorization method.

In the factorization method, first take the numbers, 1 and 70 as factors of 70 and proceed with finding the other pair of multiples of 70 which gives the results as an original number. To understand this method in a better way, read the article below to find factor 70 in pairs and also the division method to find the prime factors of 70 is discussed.

## Pair Factors of 70

To find the pair factors of 70, multiply the two numbers in a pair to get the original number as 70, such numbers are as follows

If 1 × 70 = 70, then (1, 70) is a pair factor of 70.

Similarly,

2 × 35 = 70, (2, 35) is a pair factor of 70

5 × 14 = 70, (5, 14) is a pair factor of 70

7 × 10 = 70, (7, 10) is a pair factor of 70

Therefore, the positive pair factors of 70 are (1, 70), (2, 35), (5, 14), and (7, 10)

To find the negative pair factors of 70, then proceed with the following steps

If -1 × -70 = 70, then (-1, -70) is a pair factor of 70.

Similarly,

-2 × -35 = 70, (-2, -35) is a pair factor of 70

-5 × -14 = 70, (-5, -14) is a pair factor of 70

-7 × -10 = 70, (-7, -10) is a pair factor of 70

Therefore, the negative pair factors of 70 are (-1, -70), (-2, -35), (-5, -14), and (-7, -10)

### How to calculate the Factors of 70?

Learn the following steps to calculate the factors of 70.

• First, write the number 70
• Find the two numbers, which gives the result as 70 under the multiplication, say 2 and 35, such as 2 × 35 = 70.
• We know that 2 is a prime number has only two factors, i.e., 1 and the number itself (1 and 2) which cannot be further factorized.
• 2 = 2 × 1

• But look at the number 35, which is a composite number but not a prime number and it can be further factorized.
• 35 can be factored as 5 x 7 x 1

• Therefore, the factorization of 70 is written as 70 = 7 x 5 x 2 x 1
• Finally, write down all the unique numbers that are obtained as factors.
 Factors of 70 1, 2, 5, 7, 10, 14, 35, and 70

### Prime Factors of 70 By Division Method

The number 70 is a composite and it should have prime factors. Now let us know how to calculate the prime factors of 70.

Step 1: The first step is to divide the number 70 with the smallest prime factor, say 2.

70 ÷ 2 = 35

Step 2: Again if you divide 35 by 2, you will get a fractional value and proceed with the next prime number say 5.

35 ÷ 5 = 7

Step 3: You will get a fractional number if you divide 7 by 5. So continue with the next prime factor, 7

7 ÷ 7 = 1

At the end of the division process, we received the number 1. So that we cannot proceed further. So, the prime factors of 70 are written as 2 x 5 x 7, where 2, 5 and 7 are the prime numbers.

It is possible to find the exact number of factors of a number 70 with the help of prime factorisation. The prime factor of the 70 is 2 x 5 x 7. The exponents in the prime factorisation are 1, 1 and 1. Add the number 1 with the exponents and multiply it. (1+1)(1+1)(1+1) = 2 x 2 x 2= 8. Therefore, the number 70 has 8 factors.

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